{"paper":{"title":"Stochastic solutions of a class of Higher order Cauchy problems in $\\rd$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Erkan Nane","submitted_at":"2008-09-29T18:52:41Z","abstract_excerpt":"We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Allouba and Zheng \\cite{allouba1}, Baeumer, Meerschaert and Nane \\cite{bmn-07}, Meerschaert, Nane and Vellaisamy \\cite{MNV}, and Nane \\cite{nane-h}. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index $0<\\beta <1$, or by the absolute value of a symmetric $\\alpha$-stable process with $0<\\alpha\\leq 2$, independent of the Markov process. In some special cases we r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4824","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}